Analytical solutions and chaotic insights into the Hirota-Maccari system

Area of Science:

• Nonlinear Physics
• Mathematical Physics
• Optics

Background:

• The (2+1)-dimensional Hirota-Maccari (HM) model is a type of Schrödinger equation relevant to nonlinear phenomena.
• Understanding diverse nonlinear phenomena in physics, optics, fluid dynamics, and plasma physics requires robust analytical and numerical methods.

Purpose of the Study:

• To investigate the (2+1)-dimensional Hirota-Maccari model.
• To derive novel soliton solutions using the [Formula: see text]-expansion and generalized [Formula: see text]-expansion methods.
• To analyze the chaotic properties of the model.

Main Methods:

• Variable transformation to an ordinary differential equation.
• Application of [Formula: see text]-expansion and generalized [Formula: see text]-expansion methods.
• Numerical simulations in 2D, 3D, and contour formats.
• Galilean transformation for dynamic planner structure.
• Chaos detection tools (fractal dimensions, basins of attraction, recurrence maps, strange attractors, multistability, return maps).

Main Results:

• Generation of various soliton solutions including double periodic waves, dark solitons, bright solitons, anti-compacton solitons, bright dark breather waves, periodic multiple waves, multiple dark-bright breather waves, compactons, and [Formula: see text]-shaped periodic waves.
• Numerical simulations visualized in 3D and 2D formats.
• Analysis of chaotic behaviors and multistability within the model.

Conclusions:

• The [Formula: see text]-expansion and generalized [Formula: see text]-expansion methods provide new solutions for the Hirota-Maccari model.
• The study bridges theoretical understanding with potential applications in nonlinear physical systems.
• This research presents novel findings on the model's dynamics and chaotic properties.